[PDF] Top 20 Numerically Stable, Structure-preserving Algorithms for Palindromic Quadratic Eigenvalue Problems

... the palindromic quadratic eigenvalue problem as a >- symplectic pencil which preserves the reciprocity property of the ...develop numerically stable, structure-preserving ... See full document

... a palindromic QEP to a >- skew-Hamiltonian pencil by (S+S −1 ...(G>SHIRA) for solving large sparse >-skew-Hamiltonian ...standard algorithms proposed in this paper are numerically ... See full document

... . For future references, we will call PQEP ...finite eigenvalue magnitudes ranging from 10 −50 to 10 50 or to an even greater extreme; and (4) all finite nonzero eigenvalues and eigenvectors are to be ... See full document

... RRes for frequency ω = 50 and ω = 2000, ...three algorithms, but the accuracy of the eigenpairs computed by Algorithm ...two algorithms. When Algorithms 5.1, 5.2 and 5.3 are terminated ... See full document

... T-palindromic quadratic eigenvalue problems (TPQEP) arising from modeling leaky surface waves propagation in a acoustic resonator with in- finitely many periodically arranged interdigital ... See full document

... a quadratic eigenvalue problem (QEP) Q(λ)x ≡ (λ 2 B + λC + A)x = 0, (1) where A, B, C ∈ C n×n , λ ∈ C, x 6= 0 ∈ C n ...extra structure that results in certain symmetry in the ...the ... See full document

... 1 Introduction Railway travel was the first form of mass transport. After World War II, im- provements in automobiles, highways and aircrafts made them practical for a greater portion of the population, especially ... See full document

... efficient for small to medium size examples, as illustrated by numerical ...simulation. For large and structured problems, modifications to the SDA + Newton algorithm or new algorithms may ... See full document

... and palindromic approaches to dis- crete-time control ...trains, palindromic eigenvalue problems and structure-preserving doubling ... See full document

... approach for solving the eigenpairs of P(λ) in ...a palindromic linear pencil λZ ? +Z and preserves reciprocity of ...the palindromic structure in the original polynomial so that the ... See full document

... Palindromic quadratic eigenvalue problem Structure-preserving a b s t r a c t We study the generalized eigenvalue problems (GEPs) derived from modeling the surface ... See full document

... generalized eigenvalue problems (GEPs) derived from modeling the surface acoustic wave in piezoelectric materials with periodic ...T-palindromic quadratic eigenvalue problem (TPQEP), ... See full document

... This paper is organized as follows. In Section 2, we proposed a structured quadraticization to transform a (?, ε)-PPEP with the even degree into a (?, ε)-PQEP. In Section 3, we develop a ... See full document

... number for a nonzero simple eigenvalue of poly- nomial eigenvalue problem (PEP) have been investigated by Tisseur (Linear Algebra ...bers for λ and 1/λ ? of ?-PPEP are ...of ... See full document

... the Quadratic Palindromic Eigenvalue Problem (QPEP) [1, 2, 3]: find a scalar λ and an n-dimensional vector x such that (A T 1 λ 2 + A 0 λ + A 1 )x = 0, ...structurally preserving linearization ... See full document

... details. For general perturbation of eigenvalues for polynomial eigenvalue problems, see [1, ...results for general matrix polynomials, see the mas- terpiece ...of palindromic ... See full document

... data for the reduced ...a structure-preserving doubling algorithm to compute the stabilizing solution of the matrix equation X + A T X −1 A = Q, whose existence is guaranteed by a result on the ... See full document

... data for the reduced ...a structure-preserving doubling algorithm to compute the stabilizing solution of the ma- trix equation X + A T X −1 A = Q, whose existence is guaranteed by a result on the ... See full document

... polynomials, palindromic linearizations, the anti-triangular canonical form [16–18] and the semi-Schur anti-triangular canonical form is investigated by means of the Bauer–Fike technique for perturbations ... See full document

... of quadratic eigenvalue problems (QEPs) is proposed by Friswell, Inman and Pilkey 1998, to incorporate the measured model data into the finite element model to produce an adjusted finite element ... See full document